Three-dimensional multi-missile time cooperative guidance method and system based on residual neural network

Abstract

The application discloses a three-dimensional multi-missile time cooperative guidance method and system based on a residual neural network, relates to the technical field of precision guidance, and comprises the following steps: S1, a three-dimensional multi-missile cooperative guidance closed-loop system is decomposed into a fast subsystem and a slow subsystem; S2, an augmented proportional guidance law of the fast subsystem is designed; S3, a communication topology of the multi-missile is modeled as an undirected connected graph, a remaining flight time TGO deviation is calculated, and a discrete-time consensus protocol is designed; S4, a predictor neural network PredictorNN with a residual structure is constructed; S5, a multi-objective reward function with a dynamic weight scheduling is designed; and S6, a posterior verification and retry mechanism is set. The three-dimensional multi-missile time cooperative guidance method and system based on the residual neural network solve the problems of incomplete dynamics representation, large collision time error and limited robustness in the prior art.

Description

Technical Field

[0001] This invention relates to the field of precision guidance technology, and in particular to a three-dimensional multi-missile time-coordinated guidance method and system based on residual neural networks. Background Technology

[0002] In modern military systems, missiles are one of the core weapon systems. Multi-missile coordinated interception can significantly improve the probability of striking high-value targets. Time-coordinated guidance is a key technology for achieving simultaneous interception of multiple missiles. Its core is to coordinate the remaining time of flight (TGO) of each missile to ensure that multiple missiles hit the target at the same time.

[0003] Currently, three-dimensional multi-missile time-coordinated guidance mainly falls into two technical paradigms: one is independent guidance without inter-missile communication, where each missile autonomously adjusts its guidance commands to match the time-of-flight (TGO) to a preset value; the other is coordinated guidance based on inter-missile communication networks, where missiles exchange status information (relative position, velocity, remaining time estimate, etc.) in real time and adjust their motion states through a consensus protocol to achieve TGO convergence. However, both paradigms have significant technical defects: First, the dynamic characterization is incomplete: traditional methods do not decompose the guidance system into time scales, and the rapidly changing missile-target relative motion is coupled with the slowly changing multi-missile time coordination, making it difficult to balance stability and coordination accuracy in guidance law design; second, the TGO estimation error is large: affected by differences in missile initial states, uncertainties in dynamic models, and changes in the relative geometry of missiles and targets, TGO estimation has systematic biases and outliers, leading to non-negligible collision time errors; third, the robustness is limited: facing complex scenarios such as extreme initial position conditions and target maneuvers (sudden velocity changes), the time coordination error of traditional methods will increase sharply, even resulting in interception failure, failing to meet the requirements of actual combat.

[0004] To address the aforementioned issues, existing technologies attempt to introduce neural networks to optimize TGO estimation, such as using LSTM networks to predict target maneuver trajectories and designing guidance bias terms based on deep reinforcement learning. However, these methods still have shortcomings: First, they do not systematically decompose the time-scale characteristics of three-dimensional guidance, and the neural network is only used as an auxiliary module, not deeply integrated with the guidance law; second, the use of ordinary multilayer perceptrons (MLPs) is prone to gradient vanishing, making it difficult to learn the nonlinear dynamics of TGO errors; and third, they lack a closed-loop error correction mechanism, making it impossible to effectively optimize for extreme error scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a three-dimensional multi-missile time-coordinated guidance method and system based on residual neural networks, which solves the problems of incomplete dynamic characterization, large collision time error and limited robustness in existing technologies.

[0006] To achieve the above objectives, this invention provides a three-dimensional multi-missile time-coordinated guidance method based on residual neural networks, comprising the following steps: S1. The three-dimensional multi-missile cooperative guidance closed-loop system is decomposed into fast subsystem and slow subsystem through singular perturbation theory; the missile-target relative motion loop is represented by the fast subsystem, and the coordination loop of multi-missile time coordination is represented by the slow subsystem. S2. Design the augmented proportional guidance law (APN) of the fast subsystem, ensure the input state stability (ISS) of the fast subsystem, and generate missile lateral acceleration commands. S3. Model the communication topology of multiple missiles as an undirected connected graph, calculate the remaining flight time TGO deviation, and design a discrete-time consistency protocol. S4. Construct a residual structure prediction neural network PredictorNN, taking the missile's three-dimensional initial position as input and the predicted interception time cooperative error as output, and train PredictorNN. After training, predict and compensate for the system bias and outliers of TGO estimation. S5. Design a multi-objective reward function with dynamic weight scheduling. Adaptively adjust the weights of each optimization objective in the reward function according to the prediction error level of PredictorNN to achieve a dynamic trade-off between time-coordinated accuracy and interception performance. S6. Set up a post-test verification and retry mechanism to verify the time coordination error of the actual interception, and perform parameter optimization and retry for extreme error scenarios that exceed the threshold, so as to realize the time coordination guidance of three-dimensional multi-missiles and ensure that multiple missiles intercept the target simultaneously.

[0007] This invention also provides a system for a three-dimensional multi-missile time-coordinated guidance method based on residual neural networks, including a fast subsystem guidance module, a slow subsystem coordination module, a residual network prediction module, a dynamic weight scheduling module, and a posterior verification optimization module. Each module is connected in sequence to form a closed-loop guidance system to realize the above-mentioned guidance method. The fast subsystem guidance module is used to implement the augmented proportional guidance law, generate lateral acceleration commands, and ensure the stability of the missile-target relative motion loop's ISS. The slow subsystem coordination module is used to implement the discrete-time consistency protocol, generate longitudinal coordinated acceleration commands, and achieve consistent convergence of multi-missile TGO. The residual network prediction module is used to build and train PredictorNN; The dynamic weight scheduling module is used to design multi-objective reward functions and schedule weights, dynamically balancing time coordination accuracy and interception performance. The posterior verification optimization module is used to implement posterior verification and retry mechanisms, and to perform verification, retry, and incremental learning for extreme error scenarios.

[0008] Therefore, the present invention employs the above-mentioned three-dimensional multi-missile time-coordinated guidance method and system based on residual neural networks, which has the following beneficial effects: (1) System decomposition takes into account both stability and cooperative accuracy: The guidance system is decomposed into fast and slow subsystems using singular perturbation theory. The fast subsystem ensures the stability of ISS through the APN guidance law, and the slow subsystem achieves TGO convergence through the consensus protocol, which solves the problem of incomplete dynamic characterization in traditional methods. (2) Residual network reduces TGO estimation error: The residual structure PredictorNN accurately predicts the TGO error trend through the "gradient highway" and ODE incremental learning characteristics. According to Monte Carlo simulation, the average collision time difference of this invention is as low as 0.023s, which is far better than the 0.107s of the traditional APN method. (3) Dynamic weight scheduling achieves scene adaptation: The tiered weight scheduling strategy dynamically adjusts and optimizes the priority according to the prediction error level, balances performance in normal scenarios, and prioritizes time coordination in complex scenarios, so as to achieve adaptive guidance in different scenarios. (4) Closed-loop verification optimization improves robustness: The "prediction-adjustment-verification" closed-loop mechanism performs retry and incremental learning for extreme error scenarios. Under extreme initial position conditions, the average time difference is reduced from 2.28s in the traditional APN method to 0.2202s, and the proportion of severe extreme errors (y>0.5s) is reduced from 65.78% to 10.52%, significantly improving robustness; (5) Strong engineering practicality: PredictorNN is a lightweight network with fast forward propagation inference speed, which can meet the real-time guidance requirements; the retry mechanism is executed offline, without the need to modify the guidance logic of the actual missile, and is easy to implement in engineering.

[0009] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0010] Figure 1 This is an overall flowchart of the three-dimensional multi-missile time-coordinated guidance method based on residual neural networks of the present invention; Figure 2 This is a schematic diagram of the relative motion between the missile and the target according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the residual block structure according to an embodiment of the present invention; Figure 4 This is a comparison chart of the training loss of the MLP before and after the residual network improvement in this embodiment of the invention; Figure 5 This is a schematic diagram of the time difference and interception distance distribution in a Monte Carlo simulation according to an embodiment of the present invention; wherein (a) is a schematic diagram of the time difference distribution and (b) is a schematic diagram of the interception distance distribution; Figure 6 The following are missile trajectory and parameter variation curves under extreme initial conditions according to an embodiment of the present invention; wherein (a) is a three-dimensional interception trajectory diagram, (b) is an altitude profile diagram, (c) is a missile velocity profile diagram, and (d) is an APN guidance acceleration diagram. Detailed Implementation

[0011] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0012] Example 1 Please see Figures 1-6 A three-dimensional multi-missile time-coordinated guidance method based on residual neural networks includes the following steps: S1. The three-dimensional multi-missile cooperative guidance closed-loop system is decomposed into fast subsystem and slow subsystem through singular perturbation theory; the missile-target relative motion loop is represented by the fast subsystem, and the coordination loop of multi-missile time coordination is represented by the slow subsystem. S11. The system state vector is divided into a slow state vector representing the missile's remaining flight time TGO and a fast state vector representing the missile-target relative motion, and singular perturbation parameters are introduced. The coupled dynamical system is transformed into a standard singular perturbation form, expressed as: ; In the formula, Represents the slow state vector. , Indicates the first The remaining flight time of the missiles; Indicates the missile number. ; Indicates the number of missiles. That is, there are a total of 3 missiles; Indicates transpose; Represents the fast state vector. , Indicates the first The relative position vector between the missile and the target Indicates the first The relative velocity vector between the missile and the target. Indicates the first The line-of-sight angle variable or line-of-sight direction vector corresponding to each missile. ; , express It is a three-dimensional real vector. Represents the target position vector. Indicates the first The position vector of each missile; express transpose, express transpose, express transpose; Describes the singular perturbation parameters, satisfying ; Represents the dynamics function of the slow subsystem; Represents the dynamics function of the tachyon system; This indicates the longitudinal coordinated control command for the slow subsystem; This indicates the lateral acceleration command for the tachy subsystem; S12. Based on Tikhonov's theorem, the stability of the fast subsystem and the slow subsystem is analyzed independently, and the three-dimensional relative motion dynamic equation of the fast subsystem and the error equation of the slow subsystem are constructed. The expression for the three-dimensional relative motion dynamic equations of the tachyon system is as follows: ; ; ; In the formula, Represents the target velocity vector; Indicates the first The velocity vector of a missile; Indicates the first Lateral acceleration command for each missile; Indicates the first Longitudinal coordinated acceleration command for each missile; Represents the gravitational acceleration vector; Indicates the first The line-of-sight rotation vector or line-of-sight angular velocity vector corresponding to each missile; The expression for the error equation of the slow subsystem is: ; In the formula, The time coordination error vector of the slow subsystem is used to characterize the deviation of the remaining flight time (TGO) of each missile from the average TGO of the missile group. Represents the time-coordinated error vector The derivative with respect to time; This represents the adaptive gain function of the PredictorNN neural network output by the residual structure; This represents the initial spatial distribution or initial position vector of multiple missiles; This represents the Laplace matrix corresponding to the multi-missile communication topology diagram.

[0013] S2. Design the augmented proportional guidance law (APN) of the fast subsystem, ensure the input state stability (ISS) of the fast subsystem, and generate missile lateral acceleration commands. S21. Design the augmented proportional guidance law (APN) of the fast subsystem to generate the missile's lateral acceleration command, the expression of which is: ; In the formula, Represents navigation constants, and ; Indicates the closing velocity; This represents the line-of-sight angular velocity vector; Represents a unit vector perpendicular to the line of sight; This represents the component of the target's acceleration perpendicular to the line of sight; S22. Select a Lyapunov candidate function, differentiate it with respect to time and substitute it into the APN guidance law to verify that the line-of-sight angular velocity is eventually bounded under the bounded target maneuvering disturbance and converges to a bounded neighborhood near the origin. The expression for the Lyapunov candidate function is: ; In the formula, Indicates the first Lyapunov candidate functions for a missile tachyon system are used to measure the line-of-sight angular velocity error energy. The expression obtained by differentiating with respect to time and substituting it into the APN guidance law is: ; In the formula, This represents the projection of the target's maneuvering acceleration onto the plane normal to the line of sight; Indicates the first The closed-loop velocity between the missile and the target; the first term on the right side of the equation is a negative definite term, and the second term is a bounded term. bounded).

[0014] S3. Model the communication topology of multiple missiles as an undirected connected graph, calculate the remaining flight time TGO deviation, and design a discrete-time consistency protocol. S31. Communication Topology Modeling: Defining Node Sets Adjacency Matrix , , , and Let represent the nodes of the 1st, 2nd, and 3rd missiles in the communication topology graph, respectively, and their adjacency matrices. Non-zero elements are set to 1, generating an undirected connected graph. , , This represents the set of communication edges, that is, which missiles have information exchange relationships; S32. Calculate the deviation of the remaining flight time of each missile relative to the mean of the missile group, i.e., the TGO deviation, to obtain the time coordination error vector. definition The set of TGO estimates at each step is as follows The average TGO of the missile group is , , Time-coordinated error vector The expression is: ; In the formula, Represents a vector consisting entirely of 1s; S33, Laplace matrix based on undirected connected graphs Design a discrete-time consensus protocol to drive the asymptotic convergence of the time coordination error of the slow subsystem; The iterative form of the discrete-time consensus protocol is expressed as follows: ; ; In the formula, express; Represents the identity matrix; Denotes the step size, satisfying , Represents the Laplace matrix The largest eigenvalue; The discrete-time consensus protocol guarantees that the time-coordinated error vector asymptotically converges to 0. To achieve consistency in TGO of multiple missiles.

[0015] S4. Construct a residual structure prediction neural network PredictorNN, taking the missile's three-dimensional initial position as input and the predicted interception time cooperative error as output, and train PredictorNN. After training, predict and compensate for the system bias and outliers of TGO estimation. S41. Network Structure Design: [The following text appears to be incomplete and requires further context:] The three-dimensional initial position information of each missile is flattened into a 9-dimensional vector. As input to PredictorNN, the interception time collaborative error will be predicted. As the output of PredictorNN; , This indicates the initial position coordinates of missile number 0. This indicates the initial position coordinates of missile number 1. This represents the initial position coordinates of missile number 2; the network consists of multiple residual blocks, with the last layer being a fully connected layer; each residual block is composed of a fully connected layer + ReLU activation function + identity mapping; the output of the residual block is... , This represents the mapping result of the weight layer. Indicates the first The network weight parameters of a layer are usually weight matrices. Indicates the first Layer activation value; The expression for the predicted interception time coordination error is: ; In the formula, Indicates the learnable parameters of the network; This represents the input-output mapping function of PredictorNN; S42. Constructing Training Samples: Generate 500 sets of training samples through Monte Carlo simulation, and randomly initialize the missile's initial position, such as... The simulation of three-dimensional multi-missile interception was run multiple times, and the data from each run was used as a set of samples. The data included the missile's initial position vector. Coordination error with actual interception time All missile interception anomalies were treated as valid samples to form a dataset. , ; Indicates the index of valid samples. Indicates the number of valid samples; S43. Using the mean squared error (MSE) as the loss function, set the training parameters, and train PredictorNN using the Adam optimizer until the loss is less than 0.003, thus obtaining the trained PredictorNN. The expression for the loss function is: ; In the formula, This represents the mean squared error loss function; Indicates the first The actual interception time coordination error corresponding to each training sample; Indicates that PredictorNN is for the first... The collaborative error of predicted interception time output from each training sample; Set the training parameters as follows: batch size=16, learning rate. The training epochs are 200, and the Adam optimizer parameters are... , and ; , and , respectively, represent the exponential decay rate of the first moment estimate of the Adam optimizer, the exponential decay rate of the second moment estimate of the Adam optimizer, and a small constant used to avoid the denominator being zero and to improve numerical stability; S44. The residual blocks of PredictorNN construct a "gradient highway" through identity mapping to avoid the gradient vanishing problem in deep networks. At the same time, the residual blocks are discretized using the forward Euler form of the ordinary differential equation ODE. This enables incremental learning of TGO error dynamics; Indicates hidden state The rate of continuous change along the network depth direction; Represents continuous depth The hidden feature state at the location; This represents the nonlinear mapping or continuous depth dynamic vector field corresponding to the residual block.

[0016] S5. Design a multi-objective reward function with dynamic weight scheduling. Adaptively adjust the weights of each optimization objective in the reward function according to the prediction error level of PredictorNN to achieve a dynamic trade-off between time-coordinated accuracy and interception performance. S51. Design a multi-objective reward function with dynamic weighted scheduling, expressed as follows: ; In the formula, Represents the reward function; Indicates time-coordination weights; This represents the absolute value of the time coordination error; Indicates the interception distance weight; Indicates relative distance; Indicates the weight of velocity profile deviation; Represents the missile velocity vector; This indicates the ideal speed required to meet the preset interception time. ; This indicates the control energy weight; Indicates the longitudinal cooperative acceleration command norm; , and All are normalization constants, representing the normalization coefficients for the distance term, velocity deviation term, and control energy term, respectively. , , ; S52. Cooperative error of prediction interception time based on the output of PredictorNN Error levels are categorized, and adjustments are made using a tiered dynamic weighting scheduling strategy. , and Fixed at 0.5; set extreme error direct transmission channel, if historical records show a certain initial position If the prediction stage is skipped, the enhancement level weight scheduling is triggered directly to avoid missed predictions by the prediction model; the expression for the tiered dynamic weight scheduling strategy is: ; In the formula, The unit of time is seconds. This indicates a retry phase triggered after a posterior validation fails. In normal scenarios, , Balancing time coordination with interception accuracy; enhancing scenarios, , Prioritize ensuring time coordination; during the retry phase, To maximize the strength of time constraints; weighted scheduling also considers the physical limits of the missile, through Penalties are used to prevent control instruction saturation; enhanced level-weighted scheduling is implemented. Time-coordination weights The value was increased from the standard 10.0 to 50.0 to enhance the penalty for timing coordination errors.

[0017] S6. Set up a post-verification and retry mechanism to verify the actual interception time coordination error, perform parameter optimization and retry for extreme error scenarios exceeding the threshold, realize three-dimensional multi-missile time coordination guidance, and ensure that multiple missiles intercept the target simultaneously. S61. Post-hoc verification: After executing the interception simulation, calculate the actual time coordination error. Set verification threshold ,like If so, guidance is complete; if If this occurs, a retry mechanism is triggered; the expression for calculating the actual time coordination error is: ; S62, Retry Mechanism: Set to 100.0, keep the other weights unchanged, and reuse the initial parameters of the missile and target, including... , , and Rerun the guidance simulation, setting the maximum number of retries to 2; S63. Incremental Learning: If the actual time coordination error is still greater than the verification threshold after triggering the retry mechanism twice, the initial position, target parameters and actual time coordination error in this scenario are recorded as extreme failure samples for offline incremental training of PredictorNN to optimize the model's extreme scenario adaptability.

[0018] Please see Figure 3 The system of the three-dimensional multi-missile time-coordinated guidance method based on residual neural network includes a fast subsystem guidance module, a slow subsystem coordination module, a residual network prediction module, a dynamic weight scheduling module, and a posterior verification optimization module. Each module is connected in sequence to form a closed-loop guidance system to realize the above guidance method. The fast subsystem guidance module is used to implement the augmented proportional guidance law, generate lateral acceleration commands, and ensure the stability of the missile-target relative motion loop ISS; The slow subsystem coordination module is used to implement the discrete-time consistency protocol, generate longitudinal coordinated acceleration commands, and achieve consistent convergence of multi-missile TGO. The slow subsystem coordination module includes a communication topology modeling unit, a TGO deviation calculation unit, and a consensus protocol execution unit. The communication topology modeling unit models the multi-missile communication network as an undirected connected graph and constructs a Laplace matrix. The TGO deviation calculation unit calculates the deviation of each missile's remaining flight time relative to the missile group's mean and generates a time coordination error vector. The consensus protocol execution unit generates a longitudinal coordination acceleration command based on the discrete-time consensus protocol, driving the time coordination error vector to asymptotically converge. The residual network prediction module is used to construct and train PredictorNN; The residual network prediction module includes a data acquisition unit, a network training unit, and an error prediction unit. The data acquisition unit generates initial data through Monte Carlo simulation and selects valid samples to form a dataset. The network training unit uses the mean squared error as the loss function and trains the residual neural network using the Adam optimizer; the error prediction unit receives the missile's initial position vector and outputs the predicted interception time cooperative error. ; The dynamic weight scheduling module is used to implement the design of multi-objective reward functions and weight scheduling, dynamically balancing time coordination accuracy and interception performance; The posterior verification optimization module is used to implement posterior verification and retry mechanisms, and to perform verification, retry, and incremental learning for extreme error scenarios.

[0019] Example 2: Simulation Verification Performance Comparison in Typical Scenarios: To verify the effectiveness of this invention, 1000 rounds of Monte Carlo simulations were conducted. The control groups were the traditional APN method and the PredictorNN+APN method. Four core metrics were compared: average time difference, standard deviation of time difference, hit rate, and average interception distance. Performance under extreme initial position conditions was also tested. Please refer to Table 1. The average time difference and standard deviation of this invention are significantly lower than those of the control group, with a higher hit rate and comparable interception distance. While maintaining high interception accuracy, it significantly improves time coordination accuracy.

[0020] Table 1

[0021] Performance comparison in extreme initial position scenarios: The extreme scenario is when three missiles launched in sequence fail to hit simultaneously or the average time difference is greater than 0.3s. The test results for the extreme scenario are shown in Table 2. The average time difference, error rate, and proportion of severe extreme errors of this invention in the extreme scenario are much lower than those of the control group. The hit rate is improved compared with PredictorNN+APN, while the error rate drops sharply to 1.9% compared with APN. The occurrence rate of severe extreme cases drops directly from 65.78% to 10.52%, which means that the robustness is significantly improved.

[0022] Table 2

[0023] Therefore, this invention employs the aforementioned three-dimensional multi-missile time-coordinated guidance method and system based on residual neural networks. It uses singular perturbation theory to decompose the guidance system into fast and slow subsystems. The fast subsystem ensures ISS stability through the APN guidance law, while the slow subsystem achieves TGO convergence through a consensus protocol, solving the problem of incomplete dynamic representation in traditional methods. The residual structure PredictorNN accurately predicts the TGO error trend through the "gradient highway" and ODE incremental learning characteristics. Monte Carlo simulation verification shows that the average collision time difference of this invention is as low as 0.023s, far superior to the 0.107s of the traditional APN method. The tiered weight scheduling strategy is based on the prediction error level. The system dynamically adjusts and optimizes priorities, balancing performance in routine scenarios and prioritizing time coordination in complex scenarios to achieve adaptive guidance under different conditions. A closed-loop "prediction-adjustment-verification" mechanism performs retrying and incremental learning for extreme error scenarios. Under extreme initial position conditions, the average time difference is reduced from 2.28s in the traditional APN method to 0.2202s, and the proportion of severe extreme errors (y>0.5s) is reduced from 65.78% to 10.52%, significantly improving robustness. PredictorNN is a lightweight network with fast forward propagation inference speed, meeting real-time guidance requirements. The retry mechanism is executed offline, requiring no modification to the actual missile's guidance logic, making it easy to implement in engineering.

[0024] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A three-dimensional multi-missile time-coordinated guidance method based on residual neural networks, characterized in that, Includes the following steps: S1. The three-dimensional multi-missile cooperative guidance closed-loop system is decomposed into fast subsystem and slow subsystem through singular perturbation theory; the missile-target relative motion loop is represented by the fast subsystem, and the coordination loop of multi-missile time coordination is represented by the slow subsystem. S2. Design the augmented proportional guidance law (APN) of the fast subsystem, ensure the input state stability (ISS) of the fast subsystem, and generate missile lateral acceleration commands. S3. Model the communication topology of multiple missiles as an undirected connected graph, calculate the remaining flight time TGO deviation, and design a discrete-time consistency protocol. S4. Construct a residual structure prediction neural network PredictorNN, taking the missile's three-dimensional initial position as input and the prediction interception time cooperative error as output, and train PredictorNN. S5. Design a multi-objective reward function with dynamic weight scheduling. Adaptively adjust the weights of each optimization objective in the reward function according to the prediction error level of PredictorNN to achieve a dynamic trade-off between time-coordinated accuracy and interception performance. S6. Set up a post-test verification and retry mechanism to verify the time coordination error of the actual interception, and perform parameter optimization and retry for extreme error scenarios that exceed the threshold, so as to realize the time coordination guidance of three-dimensional multi-missiles and ensure that multiple missiles intercept the target simultaneously.

2. The three-dimensional multi-missile time-coordinated guidance method based on residual neural networks according to claim 1, characterized in that, The specific content of S1 is as follows: S11. The system state vector is divided into a slow state vector representing the missile's remaining flight time TGO and a fast state vector representing the missile-target relative motion. Singular perturbation parameters are introduced to transform the coupled dynamics system into a standard singular perturbation form, expressed as: ； In the formula, Represents the slow state vector. , Indicates the first The remaining flight time of the missiles; Indicates the missile number. ; Indicates the number of missiles; Indicates transpose; Represents the fast state vector. , Indicates the first The relative position vector between the missile and the target Indicates the first The relative velocity vector between the missile and the target. Indicates the first The line-of-sight angle variable or line-of-sight direction vector corresponding to each missile. ; , express It is a three-dimensional real vector. Represents the target position vector. Indicates the first The position vector of each missile; express transpose, express transpose, express transpose; Describes the singular perturbation parameters, satisfying ; Represents the dynamics function of the slow subsystem; Represents the dynamics function of the tachyon system; This indicates the longitudinal coordinated control command for the slow subsystem; This indicates the lateral acceleration command for the tachy subsystem; S12. Based on Tikhonov's theorem, the stability of the fast subsystem and the slow subsystem is analyzed independently, and the three-dimensional relative motion dynamic equation of the fast subsystem and the error equation of the slow subsystem are constructed. The expression for the three-dimensional relative motion dynamic equations of the tachyon system is as follows: ； ； ； In the formula, Represents the target velocity vector; Indicates the first The velocity vector of a missile; Indicates the first Lateral acceleration command for each missile; Indicates the first Longitudinal coordinated acceleration command for each missile; Represents the gravitational acceleration vector; Indicates the first The line-of-sight rotation vector or line-of-sight angular velocity vector corresponding to each missile; The expression for the error equation of the slow subsystem is: ； In the formula, The time coordination error vector of the slow subsystem is used to characterize the deviation of the remaining flight time (TGO) of each missile from the average TGO of the missile group. Represents the time-coordinated error vector The derivative with respect to time; This represents the adaptive gain function of the PredictorNN neural network output by the residual structure; This represents the initial spatial distribution or initial position vector of multiple missiles; This represents the Laplace matrix corresponding to the multi-missile communication topology diagram.

3. The three-dimensional multi-missile time-coordinated guidance method based on residual neural networks according to claim 2, characterized in that, The specific content of S2 is as follows: S21. Design the augmented proportional guidance law (APN) of the fast subsystem to generate the missile's lateral acceleration command, the expression of which is: ； In the formula, Represents navigation constants, and ; Indicates the closing velocity; This represents the line-of-sight angular velocity vector; Represents a unit vector perpendicular to the line of sight; This represents the component of the target's acceleration perpendicular to the line of sight; S22. Select a Lyapunov candidate function, differentiate it with respect to time and substitute it into the APN guidance law to verify that the line-of-sight angular velocity is eventually bounded under the bounded target maneuvering disturbance and converges to a bounded neighborhood near the origin. The expression for the Lyapunov candidate function is: ； In the formula, Indicates the first Lyapunov candidate functions for a missile tachyon system are used to measure the line-of-sight angular velocity error energy. The expression obtained by differentiating with respect to time and substituting it into the APN guidance law is: ； In the formula, This represents the projection of the target's maneuvering acceleration onto the plane normal to the line of sight; Indicates the first The closing velocity between a missile and its target.

4. The three-dimensional multi-missile time-coordinated guidance method based on residual neural networks according to claim 3, characterized in that, The specific content in S3 is as follows: S31. Communication Topology Modeling: Defining Node Sets Adjacency Matrix , , , and Let represent the nodes of the 1st, 2nd, and 3rd missiles in the communication topology graph, respectively, and their adjacency matrices. Non-zero elements are set to 1, generating an undirected connected graph. , , Represents the set of communication edges; S32. Calculate the deviation of the remaining flight time of each missile relative to the mean of the missile group, i.e., the TGO deviation, to obtain the time coordination error vector. definition The set of TGO estimates at each step is as follows The average TGO of the missile group is , , Time-coordinated error vector The expression is: ； In the formula, Represents a vector consisting entirely of 1s; S33, Laplace matrix based on undirected connected graphs Design a discrete-time consensus protocol to drive the asymptotic convergence of the time coordination error of the slow subsystem; The iterative form of the discrete-time consensus protocol is expressed as follows: ； In the formula, express; Represents the identity matrix; Denotes the step size, satisfying , Represents the Laplace matrix The largest eigenvalue.

5. The three-dimensional multi-missile time-coordinated guidance method based on residual neural networks according to claim 4, characterized in that, The specific content in S4 is as follows: S41. Network Structure Design: [The following text appears to be incomplete and requires further context:] The three-dimensional initial position information of each missile is flattened into a 9-dimensional vector. As input to PredictorNN, the interception time collaborative error will be predicted. As the output of PredictorNN; , This indicates the initial position coordinates of missile number 0. This indicates the initial position coordinates of missile number 1. This represents the initial position coordinates of missile number 2; the network consists of multiple residual blocks, with the last layer being a fully connected layer; each residual block is composed of a fully connected layer + ReLU activation function + identity mapping; the output of the residual block is... , This represents the mapping result of the weight layer. Indicates the first The network weight parameters of the layer, Indicates the first Layer activation value; The expression for the predicted interception time coordination error is: ； In the formula, Indicates the learnable parameters of the network; This represents the input-output mapping function of PredictorNN; S42. Constructing Training Samples: Training samples are generated through Monte Carlo simulation. The initial missile positions are randomly initialized, and the three-dimensional multi-missile interception simulation is run multiple times. The data from each run is used as a set of samples. The run data includes the missile's initial position vector. Coordination error with actual interception time All missile interception anomalies were treated as valid samples to form a dataset. , ; Indicates the index of valid samples. Indicates the number of valid samples; S43. Using the mean squared error (MSE) as the loss function, set the training parameters, and train PredictorNN using the Adam optimizer until the loss is less than 0.003, thus obtaining the trained PredictorNN. The expression for the loss function is: ； In the formula, This represents the mean squared error loss function; Indicates the first The actual interception time coordination error corresponding to each training sample; Indicates that PredictorNN is for the first... The collaborative error of predicted interception time output from each training sample; S44. The residual blocks of PredictorNN construct a "gradient highway" through identity mapping, while the residual blocks are discretized using the forward Euler form of the ordinary differential equation ODE. This enables incremental learning of TGO error dynamics; Indicates hidden state The rate of continuous change along the network depth direction; Represents continuous depth The hidden feature state at the location; This represents the nonlinear mapping or continuous depth dynamic vector field corresponding to the residual block.

6. The three-dimensional multi-missile time-coordinated guidance method based on residual neural networks according to claim 5, characterized in that, The specific process in S5 is as follows: S51. Design a multi-objective reward function with dynamic weighted scheduling, expressed as follows: ； In the formula, Represents the reward function; Indicates time-coordination weights; This represents the absolute value of the time coordination error; Indicates the interception distance weight; Indicates relative distance; Indicates the weight of velocity profile deviation; Represents the missile velocity vector; This indicates the ideal speed required to meet the preset interception time; This indicates the control energy weight; Indicates the longitudinal cooperative acceleration command norm; , and All are normalization constants, representing the normalization coefficients of the distance term, velocity deviation term, and control energy term, respectively; S52. Cooperative error of prediction interception time based on the output of PredictorNN Error levels are categorized, and adjustments are made using a tiered dynamic weighting scheduling strategy. Set up a direct transmission channel for extreme errors; if the historical records show a certain initial position... If so, the prediction process is skipped and the enhanced level weight scheduling is triggered directly; The expression for the tiered dynamic weight scheduling strategy is: ； In the formula, The unit of time is seconds. This indicates a retry phase triggered after a posterior validation fails. In normal scenarios, , Balancing time coordination with interception accuracy; enhancing scenarios, , Prioritize ensuring time coordination; during the retry phase, To maximize the strength of the time constraint.

7. The three-dimensional multi-missile time-coordinated guidance method based on residual neural networks according to claim 6, characterized in that, The specific details of setting up the post-validation and retry mechanism in S6 are as follows: S61. Post-hoc verification: After executing the interception simulation, calculate the actual time coordination error. Set verification threshold ,like If so, guidance is complete; if If so, the retry mechanism will be triggered; The expression for calculating the actual time coordination error is: ； S62, Retry Mechanism: Set to 100.0, keep the other weights unchanged, and reuse the initial parameters of the missile and target, including... , , and Rerun the guidance simulation; S63. Incremental Learning: If the actual time coordination error is still greater than the verification threshold after triggering the retry mechanism twice, the initial position, target parameters and actual time coordination error in this scenario are recorded as extreme failure samples for offline incremental training of PredictorNN.

8. A system for a three-dimensional multi-missile time-coordinated guidance method based on residual neural networks as described in any one of claims 1-7, characterized in that, include: The fast subsystem guidance module is used to implement the augmented proportional guidance law, generate lateral acceleration commands, and ensure the stability of the missile-target relative motion loop's ISS. The slow subsystem coordination module is used to implement the discrete-time consistency protocol, generate longitudinal coordinated acceleration commands, and achieve consistent convergence of multi-missile TGO. The residual network prediction module is used to build and train PredictorNN; The dynamic weight scheduling module is used to design multi-objective reward functions and schedule weights, dynamically balancing time coordination accuracy and interception performance. The posterior verification optimization module is used to implement posterior verification and retry mechanisms, and to perform verification, retry, and incremental learning for extreme error scenarios.

9. The system of the three-dimensional multi-missile time-coordinated guidance method based on residual neural network according to claim 8, characterized in that: The slow subsystem coordination module includes a communication topology modeling unit, a TGO deviation calculation unit, and a consensus protocol execution unit. The communication topology modeling unit models the multi-missile communication network as an undirected connected graph and constructs a Laplace matrix. The TGO deviation calculation unit calculates the deviation of the remaining flight time of each missile relative to the mean of the missile group and generates a time coordination error vector. The consensus protocol execution unit generates a longitudinal cooperative acceleration command based on the discrete-time consensus protocol, driving the time cooperative error vector to converge asymptotically.

10. The system of the three-dimensional multi-missile time-coordinated guidance method based on residual neural network according to claim 9, characterized in that: The residual network prediction module includes a data acquisition unit, a network training unit, and an error prediction unit. The data acquisition unit generates initial data through Monte Carlo simulation and selects valid samples to form a dataset. The network training unit uses the mean squared error as the loss function and trains the residual neural network using the Adam optimizer; the error prediction unit receives the missile's initial position vector and outputs the predicted interception time cooperative error. .

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